Foundations can show Classic as well so that is what you may be seeing. Foundation is sort of a subcategory of Classic though they cannot cross enter both at the same show! They just have to be Foundation sealed to show in the specific Foundation classes. And even though they may be foundation sealed, technically, you are only supposed to show Foundation type in Foundation classes. Yeah it's kind of a mess lol. But that pony is much more thickly built than a Modern or ASPR which are the other types. In AMHR he is a winning stock horse because he is too thick for regular halter.
It's pretty much similar to regular halter so you should be fine! Just be prepared to be overlooked by the judges in a class because of the size differences. Bigger ponies are bigger movers and because of the rail working being viewed from a distance, small minis can look like smaller movers because of their size, even if they aren't! My 36" pony has looked like a midget plenty of times next to them in Classic.
Watch the other exhibitors on the rail work at local shows. Sometimes they will go down to the far end of the arena first, but the judge usually tells the first exhibitor where to go, or the exhibitor just goes to one end and the others that follow do the same. Normally they work the whole rail, again watch the others. If they are only using half the arena for halter, they will only trot that half. If it is a good size class, sometimes they trot the length of the lineup. If it's a small class, the judge may stop you after only a few steps. Also, what some people including myself like to do on the rail work is switch sides to keep the pony between you and the judge and fully show them off. So that means trotting on the off side in that direction.
Foundations are not supposed to be razored above the muzzle in the show ring so don't worry about that. You will want to clip close with a 30 though for a cleaner look.
Here is that same pony in Stock. He's 38" as a mini.